Istituto Nazionale di Ricerca Metrologica

Transcription

1 Istituto Nazionale di Ricerca Metrologica G. D Agostino, S. Desogus, A. Germak, C. Origlia and D. Quagliotti ABSOLUTE MEASUREMENTS OF THE FREE-FALL ACCELERATION g IN PANTELLERIA (ITALY) T.R. 76 November 2007 TECHNICAL REPORT I.N.RI.M. 1

2 ABSTRACT The work hereafter described was carried out on June 23-36, 2007 by the Istituto Nazionale di Ricerca Metrologica (INRIM) for the Istituto Nazionale di Geofisica e Vulcanologia (INGV) - Centro Nazionale Terremoti and Osservatorio Vesuviano. The experimental results of absolute measurements of the free-fall acceleration g carried out in Pantelleria are reported. Gravity measurements were performed with the new transportable absolute gravimeter IMGC-02. 2

3 CAPTIONS INDEX ABSTRACT... 2 CAPTIONS INDEX... 3 TABLES and FIGURE INDEX INTRODUCTION IMGC ABSOLUTE GRAVIMETER DESCRIPTION Measurement method Technical description MEASUREMENT UNCERTAINTY The instrumental uncertainty of the IMGC-02 absolute gravimeter EXPERIMENTAL RESULTS Khamma Porto REFERENCES

4 TABLES and FIGURE INDEX Figure 1. Picture of the new absolute gravimeter IMGC Figure 2.1. Schematic layout of the IMGC-02 Absolute Gravimeter... 7 Figure 2.2. GravisoftM manager front panel... 8 Figure 2.3. GravisoftPP post-processing front panel... 8 Table 3.1. Instrumental uncertainty of the IMGC-02 absolute gravimeter Figure Pictures of the observation station in Khamma Figure Plane of the building in Khamma Table Experimental results in Khamma Table Apparatus setup in Khamma Figure Time series in Khamma (rejected-red, accepted-white) Figure Data sets (average of 20 launches) collected in Khamma Figure Trajectory residuals (one launch-red, average-white) in Khamma Figure Density frequency graph in Khamma Figure Local barometric pressure acquired in Khamma Figure Launch chamber pressure in Khamma Figure Tide correction in Khamma Table Measurement uncertainty in Khamma Figure Pictures of the observation station in Porto Figure Plane of the building in Porto Table Experimental results in Porto Table Apparatus setup in Porto Figure Time series in Porto (rejected-red, accepted-white) Figure Data sets (average of 20 launches) collected in Porto Figure Trajectory residuals (one launch-red, average-white) in Porto Figure Density frequency graph in Porto Figure Ambient temperature acquired in Porto Figure Local barometric pressure acquired in Porto Figure Launch chamber pressure in Porto Figure Tide correction in Porto Table Measurement uncertainty in Porto

5 1 INTRODUCTION The measurement of the free-fall acceleration, g, has been performed with the new gravimeter IMGC-02. The apparatus (fig.1) is developed by INRIM /1/, and derives from that one previously realized in collaboration with the Bureau International des Poids et Mesures in Sèvres (BIPM) /2/. Several improvements characterize the IMGC-02, among them there is the automation of the instrument which allows to perform the measurement during the night, when the disturbance due to the environmental noise is minimum. All the measurement sessions have been recorded and stored in data files for postprocessing. If necessary, these files are delivered for future revision or checking. The software used is the GravisoftM 1.1 and GravisoftPP 1.1, developed and tested by INRIM. Figure 1. Picture of the new absolute gravimeter IMGC-02 5

6 2 IMGC ABSOLUTE GRAVIMETER DESCRIPTION 2.1 MEASUREMENT METHOD The free-fall acceleration g is measured by to tracking the vertical trajectory of a testbody subjected to the gravitational acceleration. The IMGC-02 absoulte gravimeter adopts the symmetric rise and falling method, where both the rising and falling trajectories of the test-mass are recorded. The raw datum consists in an array where each element represents the time correspondent to the passage of the test-body through equally spaced levels (or stations). A model function derived from the equation of motion is fitted to the raw datum in a least-squares adjustment. One of the parameter estimates is the acceleration experienced by the test-body during its flight. A measurement session consists of about 2000 launches. To assure the evaluated measurement uncertainty, the g value is obtained by averaging those launches which fulfill accepting criteria. 2.2 TECHNICAL DESCRIPTION A schematic layout of the apparatus is showed in fig The basic parts of the instrument are a Mach-Zehnder interferometer /3/ and a long-period (about 20 s) seismometer. The wavelength of a iodine stabilised He-Ne laser is used as the length standard. The inertial mass of a seismometer supports a cube-corner reflector, which is the reference mirror of the interferometer. The moving mirror of the interferometer is also a cube-corner retro-reflector and is directly subjected to the free falling motion. It is thrown upwards vertically by means of a launch pad in a vacuum chamber (about Pa). Interference fringes emerging from the interferometer are detected by a photo-multiplier. The output signal is sampled by a high-speed waveform digitizer synchronized to a Rb oscillator, used as the time standard. Equidistant stations are selected by counting a constant integer number of interference fringes (at present 1024); in particular consecutive stations are separated by a distance d = 1024 λ/2, being λ the wavelength of the laser radiation. The so called local fit method is used to time the interference signal /4/. In particular the time is computed by fitting the equation model of the interference of monochromatic waves to the interference fringe correspondent to the selected station. The space-time coordinates are processed in a least-squares algorithm, where a suitable model function is fitted to the trajectory datum. Each throw gives an estimate of the g value. A personal computer manage the instrument. The pad launch is triggered only if the system is found to be ready. In particular the software checks the pad launch state (loaded or unloaded) and the laser state (locked or unlocked). Environmental parameters such as the local barometric pressure and the temperature are acquired and stored for each launch. 6

7 seismometer interferometer photo-detector frame laser launch chamber computer electronics Figure 2.1. Schematic layout of the IMGC-02 Absolute Gravimeter The software used includes (i) the manager GravisoftM 1.1 (fig. 2.2) for driving the instrument and storing the measurement data and (ii) the post-processing GravisoftPP 1.1 (fig. 2.3) for elaborating the data-files. These programs were developed and tested on the LabVIEW8.2 platform. Geophysical corrections are applied: (i) the Earth tides and Ocean loading are computed with the ETGTAB, version 3.0, which uses the tidal potential development of Cartwright-Tayler-Edden (1973), (ii) the polar motion correction is computed starting from the daily pole coordinates x and y (rad) obtained from the International Earth Rotation Service (IERS). The measured gravity is normalized to a nominal pressure, taking into account a barometric factor f B = m s -2 mbar -1, as recommended by the IAG 1983 resolution n.9. Instrumental corrections are also applied: (i) the diffraction correction and the (ii) laser beam verticality. The g value associated to every measurement session is calculated as the average of n measurements and it is referred to a specific height from the floor surface. The measurement expanded uncertainty is evaluated according to the method of combination of uncertainties as suggested by the ISO GUM guide /5/. 7

8 Figure 2.2. GravisoftM manager front panel Figure 2.3. GravisoftPP post-processing front panel 8

9 3 MEASUREMENT UNCERTAINTY The uncertainty associated to the g measurement is evaluated by combining the contributions of uncertainty of the IMGC-02 absolute gravimeter, called the instrumental uncertainties to the contribution of uncertainty depending on the observation site. 3.1 THE INSTRUMENTAL UNCERTAINTY OF THE IMGC-02 ABSOLUTE GRAVIMETER Influence factors which are characteristic of the instrument are: vacuum level, nonuniform magnetic field, temperature gradient, electrostatic attraction, mass distribution, laser beam verticality, air gap modulation, length standard, time standard, retro-reflector balancing, radiation pressure and reference height. A detailed description of these phenomena concerning the present IMGC-02 absolute gravimeter can be found in /1/. Tab. 3.1 reports the quantitative assessment of the effect of every disturbing factor. The expanded uncertainty at the 95% confidence level (coverage factor k = 2.10 and 19 degrees of freedom) is estimated to be U = m s -2. The measurement uncertainty results from the combination of the instrument uncertainty with influence factors that are dependent from the observation site: Coriolis force, floor recoil and geophysical effects such as local barometric pressure, gravity tides, ocean loading and polar motion. Uncertainty tables, related to each observation site, are attached to the experimental results below described. 9

10 ctiinfluence parameters, x i Value Unit u i or a i Type A, s i Type B, a i Table 3.1. Instrumental uncertainty of the IMGC-02 absolute gravimeter Coreg on Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, ν i Equivalent standard uncertainty Drag effect negligible Outgassing effect negligible Non-uniform magnetic field effect negligible Temperature gradient effect m s -2 ±1.5E E-09 U 1.1E E E E-09 Effect for Electrostatic negligible Mass distribution effect m s -2 ±5.0E E-09 rectangular 8.3E E E E-09 Laser beam verticality correction 6.6E-09 m s -2 ±2.1E E E-09 rectangular 1.5E E E E-09 Air gap modulation effect negligible Laser effect m s E E E E E E-09 Index of refraction effect negligible Beam divergence correction 1.52E-07 m s E E E E E E E-08 Beam share effect unknown unknown Clock effect m s E E-09 rectangular 3.6E E E E-09 Finges timing effect negligible Finite value of speed of light effect negligible Retroreflector balancing 0.0E+00 m ±1.0E E-04 rectangular 3.3E E E E-08 Radiation Pressure effect negligible Reference height 5.0E-01 m ±5.0E E-04 rectangular 8.3E E E E-10 Corr. 1.59E-07 m s -2 Variance 1.6E-15-4 m 2 s Combined standard uncertainty, u 4.0E-08 m s -2 Degrees of freedom, ν eff (Welch-Satterthwaite formula) Confidence level, p Coverage factor, k (calculated with t-student) Expanded uncertainty, U = ku 21 95% E-08 m s -2 Relative expanded uncertainty, U rel = U/g 8.4E-09 10

11 4 EXPERIMENTAL RESULTS 4.1. KHAMMA The observation station of Khamma is located on a room of the elementary school, fig Figure Pictures of the observation station in Khamma 11

12 The position of the measurement point, referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where black square represents the laser body. Figure Plane of the building in Khamma The instrument processed and stored 999 trajectories after executing 1338 throws. The number of trajectories useful for post-processing was 599. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 10%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 160 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab

13 Table Experimental results in Khamma Observation Station: Khamma Date 2007, June Start/Stop time (UTC) 21:36:07 / 03:42:18 Geodetic longitude λ = Geodetic latitude ϕ = Topographic elevation H T = 170 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = 9.92 h Measurement rate m r = 140 h -1 Measurement drift m d = m s -2 h Total executed throws n et = 1388 Total processed and stored throws n ps = 999 Number of throws useful for post-processing n pp = 599 Temperature range T = (- -) C Local barometric pressure (mean) P = mbar χ 2 test (80% confidence level) χ 2 max = 19.8; χ 2 min = 7.0; χ 2 exp = 6.7 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 160 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, ν = 38, k = 2.03) U gm = m s -2 Vertical gradient (INGV data) at (80 120) cm γ = (???.? ±?.?) 10-8 s -2 Table Apparatus setup in Khamma Instrument orientation Laser body to? direction (see figure) Fitting Model Laser modulation Fringe visibility threshold f vt = 10% Measurements each set n ma = 20 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength λ l = m Clock frequency f c = Hz Vertical gradient input γ = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 20 Laser modulation frequency f lm = Hz Instrumental height h inst = m 13

14 The time series concerning the post-processed trajectories is reported in fig Data sets, each correspondent to the average of 20 launches, are reported in fig The apparatus experienced an oscillation of about m s -2. The averaged trajectory residuals after the measurement session are within ± m, fig Figure Time series in Khamma (rejected-red, accepted-white) Figure Data sets (average of 20 launches) collected in Khamma Figure Trajectory residuals (one launch-red, average-white) in Khamma 14

15 The histogram reported in fig represents the density frequency graph of the measurement session. The χ 2 test rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Figure Density frequency graph in Khamma The sensor used to record the ambient temperature didn t work properly. The graph reporting the ambient temperature is missing. Fig reports the local barometric pressure acquired each launch. Figure Local barometric pressure acquired in Khamma Fig and fig report respectively the launch chamber pressure and the tide correction applied during the measurement station. Figure Launch chamber pressure in Khamma 15

16 Figure Tide correction in Khamma The measurement uncertainty in Khamma is summarized in tab It includes the instrumental uncertainty reported in tab REMARKS After the measurement session the interferometer was found aligned as well as at the beginning. There is not reason for suspecting a thermal drift of the apparatus. The absolute measurement of the free-fall acceleration is considered to be correct. 16

17 CoonTable Measurement uncertainty in Khamma Influence parameters, x i Value Unit u i or a i Type A, s i Type B, a i re g ctitype of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, ν i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s -2 ±2.9E E-08 rectangular 2.8E E E E-08 Floor recoil effect negligible Barometric pressure correction -3.1E-08 m s -2 ±1.0E E E-08 rectangular 3.3E E E E-09 Tide correction -2.9E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E E-09 Polar motion correction -6.0E-09 m s -3 negligible -6.0E-09 Standard deviation of the mean value m s E E E E E E-08 Corr. -3.3E-07 m s -2 Variance 2.2E-15-4 m 2 s Combined standard uncertainty, u Degrees of freedom, ν eff (Welch-Satterthwaite formula) Confidence level, p Coverage factor, k (calculated with t-student) Expanded uncertainty, U = ku Relative expanded uncertainty, U rel = U/g 4.7E-08 m s % E-08 m s E-09 17

18 4.2 PORTO The observation station of Porto is located on a room of the elementary school, fig Figure Pictures of the observation station in Porto 18

19 The position of the measurement point, referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where black square represents the laser body. Figure Plane of the building in Porto The instrument processed and stored 856 trajectories after executing 987 throws. The number of trajectories useful for post-processing was 549. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 10%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and the estimated g value. The final g value is obtained by averaging 102 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in table

20 Table Experimental results in Porto Observation Station: Porto Date 2007, June 24 Start/Stop time (UTC) 08:20:28 / 13:12:15 Geodetic longitude λ = Geodetic latitude ϕ = Topographic elevation H T = 20 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = 4.88 h Measurement rate m r = 140 h -1 Measurement drift m d = m s -2 h Total executed throws n et = 683 Total processed and stored throws n ps = 549 Number of throws useful for post-processing n pp = 549 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar χ 2 test (80% confidence level) χ 2 max = 17.2; χ 2 min = 5.6; χ 2 exp = 17.5 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 102 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, ν = 34, k = 2.03) U gm = m s -2 Vertical gradient (INGV data 2005) at (80 120) cm γ = (???.? ±?.?) 10-8 s -2 Table Apparatus setup in Porto Instrument orientation Laser body to? direction (see figure) Fitting Model Laser modulation Fringe visibility threshold f vt = 10% Measurements each set n ma = 20 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength λ l = m Clock frequency f c = Hz Vertical gradient input γ = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 20 Laser modulation frequency f lm = Hz Instrumental height h inst = m 20

21 The time series concerning the post-processed trajectories is reported in fig Data sets, each correspondent to the average of 20 launches, are reported in fig The apparatus experienced an oscillation of about m s -2. The averaged trajectory residuals after the measurement session are within ± m, fig Figure Time series in Porto (rejected-red, accepted-white) Figure Data sets (average of 20 launches) collected in Porto Figure Trajectory residuals (one launch-red, average-white) in Porto 21

22 The histogram reported in fig represents the density frequency graph of the measurement session. The χ 2 test rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Figure Density frequency graph in Porto Fig and fig report respectively the ambient temperature and the local barometric pressure acquired each launch. Figure Ambient temperature acquired in Porto Figure Local barometric pressure acquired in Porto 22

23 Fig and fig reports respectively the launch chamber pressure and the tide correction applied during the measurement station. Figure Launch chamber pressure in Porto Figure Tide correction in Porto The measurement uncertainty in Palestrina is summarized in tab It includes the instrumental uncertainty reported in tab REMARKS The planned observation point, located at the middle of the room, showed a strong recoil effect. In particular the trajectory residuals highlighted a remarkable excitation of the resonance frequency of the seismometer inner spring. The instrument performance was significantly degraded. The relevant results are not reported because they are meaningless but collected data are available if necessary. The reported results concern a new observation point, located near the door (see fig ). During the observation session the alignment of the interferometer was affected by the horizontal displacement of the launch chamber. The measuring and fixed beams were not coaxial anymore. This was probably due to the slope of the floor. Luckily the displacement was linear and very slow, therefore it was possible to process the beginning of the session when the interferometer alignment was still acceptable. For this reason the absolute measurement of the local gravity field is considered to be correct. 23

24 CoonTable Measurement uncertainty in Porto Influence parameters, x i Value Unit u i or a i Type A, s i Type B, a i re g ctitype of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, ν i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s -2 ±2.9E E-08 rectangular 2.8E E E E-08 Floor recoil effect negligible Barometric pressure correction -3.1E-08 m s -2 ±1.0E E E-08 rectangular 3.3E E E E-09 Tide correction -2.9E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E E-09 Polar motion correction -6.0E-09 m s -3 negligible -6.0E-09 Standard deviation of the mean value m s E E E E E E-08 Corr. -3.3E-07 m s -2 Variance 2.1E-15-4 m 2 s Combined standard uncertainty, u Degrees of freedom, ν eff (Welch-Satterthwaite formula) Confidence level, p Coverage factor, k (calculated with t-student) Expanded uncertainty, U = ku Relative expanded uncertainty, U rel = U/g 4.6E-08 m s % E-08 m s E-09 24

25 REFERENCES [1] D Agostino,G., Development and Metrological Characterization of a New Transportable Absolute Gravimeter, PhD Thesis, [2] Cerutti,G., Cannizzo,L., Sakuma,A., Hostache, J., A transportable apparatus for absolute gravity measurements, In: VDI-Berichte n. 212, 1974: p. 49. [3] Germak,A., Desogus,S., Origlia,C., Interferometer for the IMGC rise-and-fall absolute gravimeter", In: Metrologia, Special issue on gravimetry, Bureau Int Poids Mesures, BIPM, Pavillon De Breteuil, F-92312, Sèvres Cedex, France, 2002, Vol. 39, Nr. 5, pp [4] D Agostino,G., Germak,A., Desogus,S., Barbato,G. A Method to Estimate the Time-Position Coordinates of a Free-Falling Test-Mass in Absolute Grvimetry, In: Metrologia Vol. 42, No. 4, pp , August [5] Guide to the Expression of Uncertainty in Measurement, BIPM, IEC, ISCC, ISO, IUPAC, IUPAP, OIML, ISO,